Equilibrium flow assignment in a single-commodity network

The paper is devoted to the analysis of non-zero commodity flows between distant from each other suppliers and consumers of some certain product. The issue is formulated in the form of a single-commodity equilibrium flow assignment problem. A single-commodity network, presented by a directed graph, models an integrated market of a certain product with multiple suppliers and consumers under linear functions of demand, supply, and transportation. An explicit form of conditions on active variables is obtained as well as an explicit form of variables themselves. An explicit form of conditions on non-zero commodity flow between suppliers and consumers will allow one to develop methodological tools for decision-making support in the field of analysis of spatial market relations in some integrated market of a certain product.